Danilo D'Ambrosio popped up 19 minutes from time to slot home after Dnipro captain Ruslan Rotan had been sent off for a second bookable offence.
An early effort from Dnipro's Yevhen Konoplyanka was the only real test for either keeper during a tight first half in Kiev.
A more urgent second-half performance saw Dnipro goalkeeper Denis Boyko produce a fine double-save shortly after the break, but the hosts could not hold firm after Rotan's dismissal.
Fredy Guarin found himself quickest to react to a defensive clearance, feeding D'Ambrosio who confidently slotted home.
The result leaves Inter top of Group F, with Qarabag and Saint-Etienne having played out a 0-0 draw.
Inter welcomed back Nemanja Vidic to the heart of a defence that has yet to concede a goal this season, although they were given a scare within the first 30 seconds.
Some good work down the left flank allowed Konoplyanka to cut inside and work an opening, only for his rasping 25-yard drive to be palmed away by Samir Handanovic.
The visitors came into the game on the back of a thumping 7-0 win over Sassuolo on Sunday, but struggled to recreate such incisiveness during an evenly contested first half.
Zdravko Kuzmanovic should have done better with a 23rd-minute chance, ignoring several good options before dragging a tame effort well wide of the post from just outside the area.
Mauro Icardi was Inter's star man at the weekend, netting a hat-trick, but was largely marshalled out of the game for much of the first half thanks to a well-drilled Dnipro defence.
The hosts were nearly rewarded for their defensive efforts after 33 minutes when Bruno Gama's cross found Douglas in the area, but the Brazilian could not keep his header down.
Kuzmanovic came close to making amends for his earlier wastefulness four minutes later, getting on the end of a teasing D'Ambrosio cross to power a header just over the bar.
Inter should have taken the lead five minutes after the break, when a teasing ball from Hernanes beat the offside trap to find Guarin, but the Colombian failed to keep his header under the crossbar.
Walter Mazzarri's men soon set about building the pressure and would have taken the lead six minutes later were it not for a terrific double-save from Boyko.
The Ukrainian was on hand to first deny D'Ambrosio's stabbed effort, before quickly recovering to parry away Icardi's follow-up from close-range.
The hosts went close themselves just after the hour mark, when the lively Konoplyanka again cut inside from the left to bend a shot just past the post.
Dnipro's challenge soon began to fade, though, and they found themselves down to 10 men when Rotan was perhaps harshly given his marching orders following a tangle with Guarin.
The visitors took full advantage four minutes later when Guarin's cross came straight back, allowing him to divert a header into the path of D'Ambrosio who finished with aplomb.
The win caps what has been an impressive start for Inter who remain unbeaten in all competitions so far this season.